For a full conformal field theory arising from two completely rational conformal nets, its coupling matrix has modular invariant if and only if the full conformal field theory has a trivial representation theory. When the two conformal nets coincide, a product of two modular invariants clearly satisfies the modular invariance property, and its decomposition rules are known under the name of fusion rules of modular invariants. Due to works of Evans-Pinto and Fuchs-Runkel-Schweigert, its interpretation as a braided product of Q-systems is known based on a relation between a full conformal field theory and a not necessarily local extension of a chiral conformal field theory. We have generalized this ``tensor product'' and its decomposition to the case where the two conformal nets are diferent. In the context of topological phase, this gives a composition of two gapped domain walls.